Laptop fans sometimes not spinning

Hi,

I've just gotten my hands on a used Dell 5300. I've just replace the thermal paste because it was old and crusty, tested the laptop by playing a 2 hr 1080p video and decided to have a listen. Was suspiciously silent so i unscrewed the cover to see that the fan was not spinning. After a few seconds the fan spun for 20 ish seconds and stopped again and didn't come back on. In the diagnostics it just keeps spinning like normal.

I know on gaming GPU's the fans only spin above 50 degrees on most higher end models.

Is this normal for a laptop and this model in particular?